Rapid prototyping models generated from machine vision data

Rapid prototyping models generated from machine vision data

Colin Bradley*

Department of Mechanical Engineering, University of Victoria, PO Box 3055, Victoria, BC, Canada V8W 3P6

Received 1 December 1999; accepted 28 September 2000

Abstract

This paper presents the development of both hardware and software systems suitable for the three-dimensional (3D)

digitization and computer modeling of objects intended for manufacture via computer numerically controlled (CNC)

machining or rapid prototyping and tooling systems. The hardware sub-system is comprised of a 3D machine vision sensor

integrated with a CNC machine tool. The software sub-system is comprised of modules capable of modeling very large 3D

data sets (termed cloud data) using a uni®ed, non-redundant triangular mesh. This representation is accomplished from the 3D

data points by a novel triangulation process. Several case studies are presented that illustrate the ef®cacy of the technique for

rapid manufacture from an initial designer's model. # 2001 Elsevier Science B.V. All rights reserved.

Keywords: Rapid manufacturing; Vision system; Surface modeling

1. Introduction

A large percentage of products are manufactured

through processes such as die-casting and injection

molding. There are approximately 15,000 mold and

die shops in the United States with, see Altan et al. [1],

an annual sales volume of US$ 20 billion. This

industry is employing new technologies to decrease

manufacturing costs, minimize production times and

quickly produce short prototype runs for product

testing. Technologies that promise to partially ful®ll

these demands are rapid prototyping, rapid tooling and

reverse engineering employing 3D machine vision as a

digitizer.

The process of capturing object form through sur-

face digitization and generation of a computer model

of the part is termed reverse engineering. The process

follows the opposite sequence of events performed in

normal design; a prototype object is generated from a

solid model. In the context of general manufacturing

methods, reverse engineering is an important process

for instances where a product initially exists as a

designer's model in a medium, such as styling foam

or modeling clay. The model's surface form must be

digitized and the data transformed to a computer-

based representation (compatible with current manu-

facturing methods). The digitization process can be

achieved through spatial measurements taken manu-

ally by a coordinate measuring machine (CMM) or

touch probe mounted on a CNC machine tool. The

manual process, while accurate, is laborious and not

suited for de®ning the more intricate and free-form

surface patches that are common in many modern

consumer products.

Computer vision systems, capable of measuring 3D

points on a surface, have many bene®cial features that

can increase the ef®ciency of the reverse engineering

process. Compared to touch probes, 3D vision systems

have the advantages of high data collection speed and

Computers in Industry 44 (2001) 159±173

* Tel.: �1-250-721-6031; fax: �1-250-721-6051.

E-mail address: [email protected] (C. Bradley).

0166-3615/01/$ ± see front matter # 2001 Elsevier Science B.V. All rights reserved.

PII: S 0 1 6 6 - 3 6 1 5 ( 0 0 ) 0 0 0 8 3 - X

non-contact measurement. The primary limitation is

the trade-off between the sensor's accuracy and depth

of ®eld and, in some cases, the cost.

A suitable CAD model can be utilized for genera-

tion of a CNC machine tool path or, if a rapid tooling

system is to be employed in manufacturing the part,

the 3D data can also be employed to produce the

necessary manufacturing data ®le (termed an `̀ .stl''

®le). A master pattern is produced in the rapid man-

ufacturing system (through stereo-lithography or

selective laser sintering) and employed to build a

silicone room temperature vulcanization (RTV) mold

from which short runs of ®nished parts can be pro-

duced through vacuum casting. Furthermore, recent

advances in materials and processes permit the pro-

duction of both bridge and hard tooling using rapid

manufacturing methods. The CAD data format neces-

sary for all rapid manufacturing systems is a poly-

hedral representation consisting of a mesh of planar

triangular facets completely covering the object. As

detailed in this work, generating the polyhedral trian-

gular mesh directly from the 3D digitized data can

further reduce product manufacturing times.

2. Modeling 3D digitized data

Data points generated by a 3D vision system can be

structured in a variety of ways depending on the

speci®c sensor used. A highly structured data format

is a range map consisting of a single z-value (height or

range) for each (x, y) pixel location in the image.

Range sensors utilizing a CCD camera generate single

view range maps. Some data structure is produced by

line scanning devices, whereas, sophisticated sensors

(mounted on coordinate measuring machines or CNC

machine tools) generate unstructured cloud data ®les

compiled from multiple views around the object. For

example, see the cloud data in Fig. 1 containing

110,000 data points collected from four views. Sur-

face data point resolution may also vary from sparse to

dense and contributes to the dif®culty in constructing

an accurate mesh. Construction of a uni®ed triangular

mesh to cloud data is a most challenging problem and

one focus of this research. Many algorithms have been

presented for planar data, or 3D data possessing some

degree of initial structure, but not for completely

unstructured data.

Parametric modeling entities, such as non-uniform

rational B-spline (NURB) curves and surfaces, are

ideal for computer-based design but are limited for

reverse engineering applications: (i) the parameteriza-

tion of 3D data is not robust enough to deliver smooth

and accurate surfaces, (ii) the overall 3D data set must

be manually segmented into discrete patches prior to

performing the surface ®tting, and (iii) the surface

patch continuity conditions (spatial and slope),

between all patches, must be ensured [2]. The trian-

gular meshing approach eliminates these problems

and can represent general object shapes, remove the

need for manual data segmentation and possesses

good computational ef®ciency.

Barnhill's [3] method for meshing planar data,

{�xi; yi� 2 R2}, employs a visibility criterion. As

shown in Fig. 2, an edge is visible from a point if

all possible lines connecting the point to the edge do

not touch or cross the existing mesh. In Fig. 2, all

visible edges, shown in bold, are connected to the

point. The process continues with the next nearest

point until all points are connected to the mesh. At

every stage in the triangulation, the mesh is closed,

containing no holes, and the boundary is convex,

containing no indentations. A Delaunay triangulation

Nomenclature

B patch boundary

Be � fbe1; . . . ; ben

g edges of a patch boundary

Bv � fbv1; . . . ;bvn

g vertices of a patch boundary

D � fd1; . . . ; dng digitized points representing S

E � fe1; . . . ;eng edges of a patch

Eti � feti1; eti2; eti3g edges of ti;Eti 2 E

Mi initial 3D triangular mesh

interpolating R

Mo optimized 3D triangular mesh

P � fp1; . . . ; png patches which collectively

form a mesh

R � fr1; . . . ; rng reduced subset of digitized

points

Rs � frs1; . . . ; rsn

g the sorted set R

So the original object surface

T � ft1; . . . ; tng the triangles that compose a

patch

V � fv1; . . . ; vng the vertices of a patch

Vti � fvti1; vti2; vti3g the vertices of a triangle tiG � fg1; g2; g3g the patch growth parameters

160 C. Bradley / Computers in Industry 44 (2001) 159±173

is subsequently achieved by making every triangular

facet in the mesh approximately equilateral. This

method cannot be extended to triangulate 3D cloud

data because any point, which is not coplanar with a

triangle, is visible to every edge of the triangle. The

2D Delaunay method was modi®ed and extended to

accommodate 3D data by a number of researchers:

Lawson [4], Choi et al. [5], Fang and Piegl [6] and

Cignoni et al. [7]. These methods examined data

arrangement in 3D space and employed geometric

reasoning to construct the triangular facet mesh

instead of Euclidean distance, between 2D points,

to determine the linkage of the data. For example,

Choi et al. [5] analyzed a vector angle between the

current point and a candidate point to determine

inclusion in the mesh.

A method for meshing a set of 3D cloud data points,

X � fx1; . . . ; xng � R3, on an unknown surface, U,

was proposed by Hoppe [8]. A surface normal vector

is calculated at every data point from a local approx-

imating plane derived from neighboring points. A

uniform and regular 3D grid of data is generated from

the normal vectors and data points. A triangular mesh

is created by connecting the points in adjacent rows

and columns present in the regularized grid. The

method is limited by the requirement that the input

data points xi must be uniformly and densely distrib-

uted across the given surface, U. The method is also

computationally intensive due to the large number of

calculations performed for each point and cannot be

used for sparse or irregularly distributed cloud data

due to errors induced by interpolating between sparse

data. This will result in erroneous data points that do not

accurately model the surface. Other researchers have

developed 3D cloud data meshing algorithms, Milroy

[9] and Turk and Levoy [10], however, they capitalize

on connectivity information inherent in the 3D data

generated by a speci®c machine vision system.

3. Three-dimensional vision system

The reverse engineering system consists of a MoireÂ

interferometer range sensor head (electro-optical

Fig. 1. Example of a 3D cloud data set containing 110,000 3D data points.

Fig. 2. Barnhill's method for triangulating a data set Ð the

visibility criterion.

C. Bradley / Computers in Industry 44 (2001) 159±173 161

information systems) mounted on a 3-axis CNC

milling machine. The milling machine mount includes

two stepper motors that rotate the sensor head in an

additional 2 degrees of freedom. Overall control is

provided by a PC-based programmable motion control

(PMC) board. The system can position the sensor head,

around an object placed on the machine tool deck,

within a total work volume of 75 cm� 50 cm� 24 cm.

3.1. Range sensor head

The sensor, shown in the photograph of Fig. 3,

utilizes a camera with a pixel resolution of

700� 500 and is positioned at a stand-off distance

of approximately 150 mm from the surface during

data collection. The ®eld of view is 50 mm� 50 mm

and data can be collected over a depth of ®eld of �/

ÿ15 mm from the stand-off point. The resolution of

the range data are determined by the pitch of the

projection grating; the pitch of two line pairs per

millimeter used here permits a resolution of

25.4 mm which is suitable for objects with surface

detail. A coarser pitch would lower the range data

resolution, due to the larger projected fringe spacing,

which is more suitable for objects (e.g. turbine blades)

possessing gradual changes in surface curvature. The

accuracy speci®cation is in the range 25.4±50.8 mm

for the above con®guration. As discussed by Besl [11],

this digital MoireÂ (with reference) system is a tech-

nologically more sophisticated version of the tradi-

tional shadow MoireÂ method.

Prior to collecting patch data from an object, the

sensor digitizes an image of a ¯at reference plate that

is etched with the same fringe pattern. This image is

stored and the range from the sensor to the target

surface is calculated, at each pixel location, by calcu-

lation of the phase shift between each fringe in the

projected image and the corresponding fringe in the

reference image. A more detailed description of data

point calculation is provided in the sensor's user

manual [12]. Other data patches are similarly acquired

and the process repeated until the entire object surface

is digitized. An on-line wire frame representation of

the patch data is available to guide the operator's

selection of the next sensor head position. Previous

research, for example Milroy [9] and Maver and

Bajcsy [13], has examined algorithms for computing

the minimum number of sensor head positions neces-

sary to digitize an object. In this instance, the sensor

head is positioned under operator control and the

software developed for modeling the overall data

set can accept overlapping patches.

3.2. Sensor positioning system

The milling machine has three computer-controlled

axes of motion: x, y, and z. The x and y axis are

physically realized in a cast iron deck which can move

in a plane measuring 75 cm� 50 cm. The z-axis is

normal to the planar deck and has a 24 cm travel.

Closed loop positioning for each machine axis is

through a dc servo motor and lead screw combination,

controlled by the PMC card, as shown in the diagram

of Fig. 4. As shown in Figs. 3 and 4, the PMC card also

controls the 8 oz-in and 12 oz-in torque stepper

motors, located on the sensor mount. These motors

provide additional sensor positioning capabilities and

each motor's driver is connected to a PMC digital

output port. In combination, the two motors can aim

the sensor in any direction below the horizontal plane

passing through the mount's axis and parallel to the

deck.

Supervisory control software was developed and

implemented on the PC to perform the following

functions:

� Integration of the patch data, generated by the

sensor in each viewing location, with the absolute

position obtained from the three CNC machine tool

motor encoders and the two rotational stepper

motors on the sensor head mount. The motorFig. 3. Photograph of the 3D-range sensor head mounted on the

CNC machine tool.


control software was written in the PMC card native

language and generates a cloud data file in one

unified global reference frame. Fig. 4 further illus-

trates the various component inter-connections.

� Providing a user interface for activating the sensor,

providing location feedback and controlling data

file storage. Digitized data from an object can be

displayed in a number of formats including ortho-

graphic and isometric views.

� Providing motor control and accepting required

sensor position through the user interface. Position

commands are passed to the custom motor control

program that calculates the number of motor shaft

turns, for each axis, to correctly position the sensor

at the desired 3D spatial coordinate. The PMC

control board executes this information.

4. Cloud data meshing algorithm

A ¯owchart illustrating the sequence of steps neces-

sary to form a complete mesh of a cloud data ®le is

presented in Fig. 5. The multiple patches of x±y±z

points, comprising the cloud data, are transferred from

the vision system to a workstation for geometric

modeling. The cloud data is visualized on the screen

and extraneous data points, erroneously collected

from the object ®xture or the machine tool deck,

are identi®ed and manually deleted. The cloud data

set is reduced (see Section 4.1) to a more manageable

size and the resulting ®le displayed on the workstation

screen. The part topology is examined to determine

the number of surface patches present and the ®rst

seed point for initial mesh generation (Section 4.2) is

selected employing the workstation user interface.

The initial mesh generation is repeated for each sur-

face patch utilizing an appropriate seed point. Upon

completion of this phase, the group of individual

meshes, each modeling a surface patch, are merged

to form one global mesh covering the entire object

surface. The ®nal step (outlined in Section 4.3) opti-

mizes the mesh in order to improve the local modeling

of physical edges and smooth the intervening mesh

surfaces.

The digitized data, D � fd1; . . . ; dng, is a set of 3D

coordinates of points, di � fxi; yi; zig 2 R3, on the

surface of the object, So. The data set D forms the

sampled representation of So; D can emanate from any

type of digitizing device and can be gathered from an

object of any shape. The triangular mesh, Mo is

constructed from D by the steps itemized above and

presented below in detail.

Fig. 4. Schematic diagram of the inter-connection between major system components.


4.1. Data reduction

Most 3D vision systems generate copious data sets;

the mini-MoireÂ sensor can gather up to 12,000 points

per square centimeter. Very large data sets are not

always required, therefore, a voxel binning method

(see Weir [14]) is used to reduce the data. Typical raw

data sets are reduced from the range [300,000±30,000]

points to the range [3000±1000] points. Voxel binning

reduces D, retaining a regular distribution of points

R � fr1; . . . ; rmg � D, by creating a maximum

bounding box, around D, in the three principle axes.

The volume is subdivided into uniform cubes, termed

voxel bins, and the data set D is allocated to the bins

and the point, di, closest to each bin's center is

retained. Data reduction results in a uniform distribu-

tion of points ri across the object surface, So, as shown

in Fig. 6, and is controlled through adjustment of two

parameters:

� Bin size: the size can be set explicitly or calculated

automatically by setting the desired number of bins.

Approximate spacing between the reduced data

points, R � fr1; . . . ; rng, is equal to the bin edge

length.

� Sparse data location: for a bin containing very few

points, the closest point to the bin center, ri, may

still be located in one corner of the bin. Such points

are discarded, to preserve the regular data distribu-

tion. Two criteria are optionally available to remove

irregular points: the maximum distance, c1, from ri

to the bin center, or the minimum distance, c2, from

ri to all neighboring retained points, r. The criteria

are expressed as a fraction of the voxel bin size, i.e.

0 � �c1; c2� � 1. If the point ri fails to meet the

chosen criteria, the point is discarded and the bin

remains empty. The choice of criteria depends on

the shape of the surface, So, and the density of the

digitized points, D. Each case must be evaluated

individually, but a criteria of c2 � 0:5 works well

for many digitized surfaces.

Fig. 5. Flowchart of the sequence of operations for generating a

global optimized mesh.

Fig. 6. Cloud data ®le size reduction utilizing voxel binning; initial

3D data set size 30,000 points, resulting 3D data set size 3000

points.


4.2. Initial mesh generation

The objective of mesh generation is to cover the

reduced point set, R, with an initial surface mesh of

triangular facets, Mi. A triangular mesh surface is

comprised of one, or several, mesh patches, pi, and

each patch is grown over R from a starting seed point,

rs 2 R. Any point can be selected as the seed and the

®rst patch, p1, expands until all points in R are meshed.

Complex objects, see Fig. 7, require each distinct

region, on the object, to be individually meshed and

all patches subsequently joined together to form a

continuous surface, Mi. The six patch mesh models a

surface possessing many complex features. The seed

point, for each patch, is typically placed at a distinct

feature, such as the tip of the nose.

The meshing process, illustrated in the ¯owchart of

Fig. 8, is initiated with the selection of a seed point, rs,

and all remaining points R form the initial set of valid

points available for triangulation. The set R is sorted in

increasing Euclidean distance from rs forming the

sorted subset Rs � frs1; . . . ; rsn

g � R. The seed point

rs becomes rs1, the next nearest point becomes rs2

, and

so on, as shown in Fig. 9(a). Data from previously

meshed patches are removed from R and only the

boundary points of existing patches remain. The

meshing process follows a sequence of steps.

� The first vertices fv1; v2; v3g, edges, {e1, e2, e3},

and triangle {t1} are created first as shown in Fig. 8.

The first three vertices, defining the first triangle t1,

are the first three sorted points, i.e. fv1;v2;v3g �frs1

;rs2;rs3g. The triangle t1 contains the edges

Et1�fet11;et12;et13g�fe1;e2;e3g and vertices Vt1�fvt11;vt12;vt13g � fv1;v2;v3g, as shown in Fig. 9(b).

� A second triangle, t2, is added to the patch, con-

sisting of t1, by connecting the next nearest point,

rs4, to t1. The patch boundary, B, now contains t1 and

t2, as shown in Fig. 10(a), and the outside edges

form the patch boundary Be � fbe1;be2

;be3;be4g �

fe1;e2;e3;e4g. The boundary can be described in

terms of the edges, Be, or the vertices Bv �fbv1

;bv2;bv3

;bv4g � fv1;v2;v3;v4g, so B � fBe;Bvg.

� The remaining points rsi2 Rs are considered in

their sorted order and each rsican be connected

to the expanding patch by creating vertex vn � rsi,

then creating triangles between vn and the patch

boundary, B, as shown in Fig. 10(b). This process

begins for vn by finding the nearest patch boundary

vertex, bvn2 Bv, and the adjacent patch boundary

vertex, bvn�1. The first potential triangle is formed

containing fvn; bvn; bvn�1

g. If this triangle is valid

meshing continues in a forward direction around the

boundary. The next triangle to be considered con-

tains the vertices fvn; bvn�1; bvn�2

g. When a triangle

is rejected, meshing returns to bvnand continues in

the reverse direction with fvn; bvn; and bvnÿ1

g. When

a second triangle is rejected, then meshing for vn

is finished, and the patch boundary B is updated,

as shown in Fig. 11. Meshing continues with

the next valid point, vn � rsi�1, until the patch

growth is limited by pre-defined boundary con-

straints.

� A patch grows until any combination of the follow-

ing two constraints are met: (i) the outer edge of the

digitized data is reached; (ii) a distinct edge within

the digitized data is reached, or an existing patch is

encountered.

Speci®c patch growth control parameters have been

devised to limit further expansion as mentioned in the

last point above. The parameters prevent invalid tri-

angles from becoming part of the mesh. The growth

parameters G � fg1; g2; g3g are as follows.

Fig. 7. The result of applying the meshing algorithm to a 3D-range

data set: six contiguous surface mesh patches de®ne the object's

form.


� Range parameter, g1: the distance between vn and

the patch boundary must be less than the range

parameter, e.g. jvn ÿ bvjj � g1. The range g1 is

typically twice the bin size employed in the voxel

binning process. This value ensures that neighbor-

ing vertices on a surface will be connected, but

triangles will not span large gaps in the digitized

data.

� Minimum triangle angle, g2: the smallest angle

within the triangle must be larger than the minimum

angle parameter, g2; typically, g2 � 5�. This pre-

vents nearly co-linear vertices from forming long,

narrow triangles. Such triangles are unwanted

because their surface normal may not accurately

match the object's local surface curvature.

� Maximum normal angle, g3: the angle between the

surface normal of the new triangle, nÄt, and the local

surface normal of the patch, nÄp, must be below the

maximum allowable angle parameter, g3. New tri-

angles are only valid if they form a sufficiently

smooth surface with the existing patch. This pre-

vents erroneous triangles from forming a sharp

Fig. 8. Flowchart of the algorithm for growing a mesh patch from a seed point.


corner where the digitized object does not contain

one. It also prevents the patch from growing around

sharp corners on the digitized object. The local

surface normal of the patch, nÄp, is calculated at

the boundary edge, bej, that connects the boundary

vertices, bvjand bvj�1

. Each boundary edge is

assigned a surface normal which is the average

normal of all the triangles which touch that edge.

As such, nÄp is a fair approximation of the local patch

surface normal. The dot product operation is used to

compare the normals, i.e. the new triangle is valid if

�~nt � ~np� � g3. Typical values for g3 are between 0

and 0.9.

Fig. 9. (a) Sorting of 3D data points in increasing geometric distance from the seed point rs1; (b) the creation of the ®rst triangular facet t1.

Fig. 10. (a) The creation of the mesh boundary B from triangular facets t1 and t2; (b) the growth of the mesh by adding a triangular facet

between the vertex vn � rs1and the boundary.

Fig. 11. Condition for concluding the patch growth at a vertex vn

and updating the patch boundary.


If no valid triangles can be created between vn and

the boundary, B, then the vertex vn is deleted, and the

point rsidoes not become a vertex of the growing

patch.

Many complex object surfaces cannot be covered

with a single triangular mesh, and require the selection

of several seed points at the center of each discrete

patch, as shown in Fig. 5. A mesh is then grown

independently from each seed point and a global

mesh, Mo, is ®nally constructed from the set. The

set of meshes is combined so that all boundary vertices

and edges are included with no overlapping regions at

the boundaries of the constituent patches. This tech-

nique removes the need to segment the entire cloud

data set at the outset; instead, a seed point on each

patch is selected and the mesh grows to the patch

boundary.

4.3. Mesh optimization

A triangular mesh surface patch must be optimized

to further improve the object representation. The

optimized mesh, Mo, contains the same vertices and

the same number of triangles as the initial mesh, Mi.

Edges, however, are spatially relocated to either

increase the mesh smoothness or enhance object edges

present in the mesh. The optimization algorithm itera-

tively examines every edge in the mesh surface, and

applies an appropriate criterion for ensuring mesh

improvement. Each non-boundary edge is shared by

two triangles, which together form a quadrilateral,

having the target edge as a diagonal. If the quadri-

lateral is convex, the target edge can be swapped to the

opposite diagonal to create two different triangles

between the same four vertices, as shown in Fig. 12.

The two optimization criteria are as follows.

1. Mesh smoothness: edge locations that maximizes

the smallest interior angle for the two triangles and

results in a mesh containing approximately equi-

lateral triangles.

2. Mesh edge enhancement: mesh edges are aligned

with the edges in the object surface to enhance

sharp features. Neighboring triangles are exam-

ined and the ®nal orientation of the target edge is

the one which minimizes the variation in surface

normals between the quadrilateral and the neigh-

boring triangles.

For either criterion, the set of edges, E, is examined

on each iteration of the algorithm until no further edge

adjustment is necessary. The best results have been

obtained by applying the criteria sequentially; the

initial mesh, Mi, is ®rst optimized for smoothness,

then optimized to enhance the features. This prevents

arti®cial features that exist in the initial mesh, but not

on the object surface, from being erroneously

enhanced.

5. Application examples

Two case studies are presented to show the utility of

this technique for producing parts through manufac-

turing methods such as injection molding. Injection

mold tooling can be produced by CNC machining

from the surface de®nition generated by this techni-

que. Computer aided manufacturing (CAM) packages

(such as the DelCAM Duct program) utilize the

polyhedral surface representation created here. Alter-

natively, the triangular facet model can be employed

to create a `̀ STL'' ®le compatible with all available

rapid prototyping systems. These systems, as

described by Jacobs [15], are now being employed

Fig. 12. The edge-swapping process that is the basis of the feature-enhancement process.


to quickly produce short run and bridge tooling from

stereolithography master models. The models are then

used to create the tooling for production of prototypes

in the end use material, typically an engineering plastic.

5.1. Toy model

The ®gurine head, shown in Fig. 7 is typical of

intricate parts injection molded for the toy industry.

The object occupies a volume of 60 mm� 40 mm�

30 mm and has a complex surface form that would be

ideal for production through stereolithography as

opposed to CNC machining. Machining would require

multiple part set-up on a 3-axis mill, whereas stereo-

lithography can produce the part, layer-by-layer, with

little dif®culty. The Pluto ®gurine is a dif®cult object

to model for three reasons.

1. The surface is too complex to be mapped to a 2D

planar domain (or any simple 3D geometric

Fig. 13. The six patches of Fig. 12 optimized with respect to a smoothness criterion (on the left) and subsequently with respect to feature

enhancement (on the right).

Fig. 14. Five mesh patches modeling the data obtained from the telephone receiver handset; the model contains no gaps in the mesh.


domain) thereby excluding the simple triangular

meshing algorithms discussed in Section 2.

2. The surface is not readily or easily divisible into a

set of simple four-sided patches as would be

required for ®tting by tensor product surfaces.

Furthermore, the tensor product surface patches

would need to be merged together ensuring C0 and

C1 continuity across all patch boundaries, for

example see Milroy [2].

3. The surface has large smooth regions interrupted

by sharp features with high surface curvature that

are problematic for any B-spline surface ®tting

due to dif®culty in knot vector creation, data point

parameterization, and control point location.

The 3D triangular meshing algorithm commenced

with voxel binning the data; the original cloud ®le of

29,798 points was reduced to 3134 points employing a

bin dimension of 1.00 mm. The ®gurine was modeled

with six patches, as shown in Fig. 7. The six patches,

in the order they were grown, are nose, top of head,

right cheek, left cheek, chin, back of head and neck.

Patch growth parameters were selected that allow

large patches, that join without gaps and without

forming erroneous triangles. The seed vertices were

selected at the regions of highest curvature, e.g. top of

the head, tip of the nose, bottom of the chin, and points

on the cheeks. Trial and error revealed that patch

growth performance is more ef®cient over high cur-

vature regions if the seed point is located at the center

of the region. A ®nal patch was located at the back of

the head to ®ll a gap in the original data set D.

The six component patches were merged into a

single mesh prior to optimization. The optimized

meshes are shown in Fig. 13. The most accurate mesh

was obtained by optimizing ®rst with the smoothing

criterion, shown on the left, then with the feature-

enhancing criterion, shown on the right. The ®nal

mesh is still smooth at regions of low curvature

(e.g. the bulbous nose) but still possesses clearly-

de®ned features (e.g. the eyebrows, nose wrinkles,

and cheeks). After some initial experimentation, opti-

mum growth parameters for each patch were selected.

The largest apparent gap in the mesh, on the throat

under the chin, was due to the incomplete digitizing of

the ®gurine. This gap in the data points was too large

for the mesh to span. The error between the optimized

mesh and the digitized points tended to be largest at

the boundaries between patches, however, if necessary

the ®tting error could be improved by manually

inserting or removing individual triangles. The max-

imum ®tting error between cloud data and the mesh

was 0.50 mm. Therefore, the overall worst-case error,

based on the sensor's worst-case stated error speci®-

cation between the object's surface and the ®tted

triangular mesh was 0.55 mm.

The initial digitized surface of 29,798 points was

®tted with an optimized mesh of 6240 triangles in

approximately 3 h. The breakdown of time for each

stage of the process was: 10 s to import and reduce the

initial data set, approximately 2 h to grow the initial

mesh over the object's surface, 21 min to perform

optimization with respect to the smoothness criterion,

and 17 min to optimize with respect to the feature

enhancement criterion.

Fig. 15. (a) Five patch mesh optimized with respect to smoothness;

(b) same mesh optimized with respect to feature enhancement.


5.2. Telephone handset

The telephone handset is an example of an indus-

trial type object with smooth surfaces, ®llets and sharp

edges. The dif®culty in ®tting a surface to the handset

is retaining the sharp edges without distorting the

rounded corners or ¯at faces. The telephone handset

is ®tted with ®ve patches. One possible meshing

scheme would be to ®t separate patches on each

distinct region of the surface. The dif®culty to this

Fig. 16. Cross-sections through the telephone receiver handset illustrating the accuracy of the surface mesh model ®t: (a) location of the cutting

planes through the object; (b) longitudinal cross-section; (c) lateral cross-section through ear-piece; (d) lateral cross-section through mouthpiece.


approach is the rounded corners which do not provide

a clear boundary between surface regions. It would be

very dif®cult to select patch growth parameters which

constrain the patches to one surface region. Instead,

three large patches were grown to cover several sur-

face faces and two smaller patches were grown to ®ll

the gaps, as illustrated in Fig. 14. The resulting mesh

has no gaps or erroneous triangles.

The telephone handset was optimized ®rst for

smoothness, then to enhance the features. The smooth

mesh, shown in Fig. 15(a), predictably results in all the

sharp features of the surface becoming bevelled. The

feature enhancement shown in Fig. 15(b) causes the

triangle edges to align with the surface features, thus

enhancing the sharp edges between the ¯at faces. This

enhancement is clearly seen around the edges of the

ear and mouth pieces of the handset.

The ®tting errors in the handset mesh are best

illustrated with cross-sections, comparing the fea-

ture-enhanced mesh with the original digitized sur-

face. Three cross-sections are examined, as shown in

Fig. 16. The longitudinal cross-section shows the

maximum errors, at the sharp edge in the top left

corner of Fig. 16. The magnitude of this error is

approximately 0.8 mm, which is approximately half

of the voxel bin size of 2 mm. Furthermore, the overall

worst case error between actual part and ®tted mesh

was 0.85 mm. The ¯at bottom of the handset was not

digitized, so the mesh does not wrap around the

handset.

The telephone handset mesh is also suitable for

manufacture by either CNC machining or rapid pro-

totyping and tooling. Since, a triangular mesh is a

common method for describing a surface, the mesh

can be translated into any suitable computer ®le

format, such as IGES, DXF, or STL.

6. Summary

This research project has resulted in a ¯exible

hardware and software system that can enable the

rapid reverse engineering of objects typically encoun-

tered in the manufacturing arena. The CNC machine

tool mounted 3D vision system is an alternative to

expensive coordinate measuring machines. The mesh-

ing algorithm provides a means of accurately model-

ing complex models in a form that is compatible with

rapid tooling and prototyping machine and CNC

milling machine requirements.

The meshing software has several advantages com-

pared to other 3D data modeling techniques.

� The data can be generated by any digitizing device

and is not dependent on any structure in the data,

that is the algorithm functions with true 3D cloud

data.

� The algorithm's operation is not limited by the

complexity of the object's surface form.

� The optimization criteria ensure that important

engineering features on an object such as edges

are preserved in their initial `̀ crisp'' form.

� Compared to parametric surface fitting, the algo-

rithm is much less reliant on operator interaction,

such as the requirement to manually define and

segment patches of surface data.

References

[1] T. Altan, B.W. Lilly, J.P. Kruth, W. Konig, H.K. Tonshoff,

C.A. van Luttervelt, A.B. Khairy, Advanced techniques for

die and mold manufacturing, Annals of the CIRP 42 (2)

(1993) 707±715.

[2] M. Milroy, C. Bradley, G.W. Vickers, G1 continuity of B-

spline surface patches in reverse engineering, Computer

Aided Design 27 (6) (1995) 471±478.

[3] R.E. Barnhill, Representation and approximation of surfaces,

in: J.R. Rice (Ed.), Mathematical Surfaces III, University of

Wisconsin, Madison, WI, USA, 1977, pp. 69±120.

[4] C.L. Lawson, Software for C1 surface interpolation,

Mathematical Software III, Academic Press, New York,

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scattered data in 3D space, Computer Aided Design 20 (5)

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sions, IEEE Computer Graphics and Applications 15 (5)

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conquer delaunay triangulation algorithm in Ed, Computer

Aided Design 30 (5) (1998) 333±341.

[8] H. Hoppe, Surface Reconstruction from Unorganized Points,

Ph.D. Thesis, University of Washington, 1994.

[9] M. Milroy, C. Bradley, G.W. Vickers, Automated laser

scanning based on orthogonal cross-sections, Machine Vision

and Applications 9 (1996) 106±118.

[10] G. Turk, M. Levoy, Zippered polygon meshes from range

images, in: Proceedings of the SIGGRAPH '94, Computer

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[11] P.J. Besl, Range imaging sensors, Research Report GMR-


6090, General Motors Research Laboratories, Michigan,

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[12] J.M. Fitts, High-speed non-contact X±Y±Z gauging and part

mapping with MoireÂ interferometry, Electro-Optical Informa-

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[13] J. Maver, R. Bajcsy, Occlusions as a guide for planning the

next view, IEEE Transactions Pattern Analysis and Machine

Intelligence 15 (5) (1993) 417±433.

[14] J. Weir, M. Milroy, C. Bradley, G.W. Vickers, Reverse

engineering physical models employing wrap around B-

spline surfaces and quadrics, Proceedings of the Institution of

Mechanical Engineers Part B 210 (1996) 147±157.

[15] P. Jacobs, Recent advances in rapid tooling from stereolitho-

graphy, in: The Seventh International Conference on Rapid

Prototyping, San Francisco, 1997, pp. 338±354.

Colin Bradley is an Associate Professor

in the Department of Mechanical Engi-

neering at the University of Victoria. He

teaches and performs research in the

design and manufacturing area. The

research focuses on the application of

emerging technologies to assist the

improvement of the design and manufac-

turing processes. Dr. Bradley received a

BASc from the University of British

Columbia, MSc from Herriot-Watt University and a PhD from

the University of Victoria. He has been an ASI Fellow since

1994 and won the NSERC Doctoral Prize in 1993. From 1997 to

1999, Dr. Bradley was a Senior Research Fellow at the National

University of Singapore.


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Rapid prototyping models generated from machine vision data